Related papers: Dense random packing with a power-law size distrib…
In this work, the well known power-law relation between strength and sample size, $d^{-n}$, is derived from the knowledge that a dislocation network exhibits scale-free behaviour and the extreme value statistical properties of an arbitrary…
We have studied using the KLUN sample of 5171 spiral galaxies having Tully-Fisher distance moduli, the average radial space distribution of galaxies out to a distance of about 200 Mpc (for H_0=50 km/s/Mpc). One motivation came from the…
We argue that a finite iteration of any surface fractal can be composed of mass-fractal iterations of the same fractal dimension. Within this assertion, the scattering amplitude of surface fractal is shown to be a sum of the amplitudes of…
We computationally study jammed disordered hard-sphere packings as large as a million particles. We show that the packings are saturated and hyperuniform, i.e., that local density fluctuations grow only as a logarithmically-augmented…
The fragmentation of a two-dimensional circular disc by lateral impact is investigated using a cell model of brittle solid. The disc is composed of numerous unbreakable randomly shaped convex polygons connected together by simple elastic…
In this paper, we perform molecular dynamics (MD) simulations to study the two-dimensional packing process of both monosized and random size particles with radii ranging from $1.0 \, \mu m$ to $7.0 \, \mu m$. The system was allowed to…
The multi-scale expansions and contractions of the Earth's magnetosphere explain fundamental issues of magnetic storm-substorm relationship. This magnetospheric behavior is in agreement with a model of 3D-spirally-faster-inward-oscillating…
The availability of neutron spallation-source instruments that provide total scattering powder diffraction has led to an increased application of real-space structure analysis using the pair distribution function. Currently, the analytical…
The densest amorphous packing of rigid particles is known as random close packing. It has long been appreciated that higher densities are achieved by using collections of particles with a variety of sizes. The variety of sizes is often…
We examine the dynamic spreading of a dense overdamped suspension of particles under power law repulsive potentials, often called Riesz gases. That is, potentials that decay with distance as 1/r^k where k\in (-2,\infty]. Depending on the…
We investigate the approach to catastrophic failure in a model porous granular material undergoing uniaxial compression. A discrete element computational model is used to simulate both the micro-structure of the material and the complex…
A new discrete distribution has been proposed as a discrete analogue of the two sided power distribution [Van Drop, J. R. and Kotz, S. (2002a). A novel extension of the triangular distribution and its parameter estimation, Journal of the…
In this article we investigate the energy spectrum statistics of fractals at the quantum level. We show that the energy-level distribution of a fractal follows a power-law behaviour, if its energy spectrum is a limit set of piece-wise…
We present a number models describing the sequential deposition of a mixture of particles whose size distribution is determined by the power-law $p(x) \sim \alpha x^{\alpha-1}$, $x\leq l$ . We explicitly obtain the scaling function in the…
The process of formation of fractal structure in one-dimensional self-gravitating system is examined numerically. It is clarified that structures created in small spatial scale grow up to larger scale through clustering of clusters, and…
We investigate the two-dimensional packing of extremely prolate (aspect ratio $\alpha=L/D>10$) granular materials, comparing experiments with Monte-Carlo simulations. The average packing fraction of particles with aspect ratio $\alpha=12$…
Using the apparatus of correlation Gamma-function (``conditional density''), we have analyzed spatial clustering of objects from several different samples of galaxies, clusters and superclusters. On small scales the distribution of objects…
Sea ice is a complex system, and observations have shown that ice segments (i.e., floes) have a wide range of sizes, with a floe size distribution that follows a power law. However, a theory for the power law and its exponent have remained…
Within the point vortex model, we compute the probability distribution function of the velocity fluctuations induced by same-signed vortices scattered within a disk according to a fractal distribution of distances to origin $\sim…
Patterns of different symmetries may arise after solution to reaction-diffusion equations. Hexagonal arrays, layers and their perturbations are observed in different models after numerical solution to the corresponding initial-boundary…